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According to the Associative Property, which expression is equivalent to 30m+(21m−53)+(18−2m) ?(1 point) Responses 53m−35 53 m minus 35 51m+(−53+18)−2m 51 m plus left parenthesis negative 53 plus 18 right parenthesis minus 2 m (30m+21m)+(18−2m) left parenthesis 30 m plus 21 m right parenthesis plus left parenthesis 18 minus 2 m right parenthesis (49m−53)+16 left parenthesis 49 m minus 53 right parenthesis plus 16

1 answer

To apply the Associative Property, we need to group the terms in a different way while maintaining their original sum. The original expression is:

\[ 30m + (21m - 53) + (18 - 2m) \]

We can rearrange, or regroup, it using the Associative Property.

Let's break it down:

  1. You can group the \( 30m \) and \( 21m \) together:

\[ (30m + 21m) + (18 - 2m - 53) \]

This translates to:

\[ 51m + (18 - 53 - 2m) \]

  1. However, based only on the options you provided, the correct expression that applies the associative property most closely while still neatly grouping terms while keeping the overall expression the same would be:

\[ (30m + 21m) + (18 - 2m) \]

Therefore, among your options, the choice that fits this example best is: \[ (30m + 21m) + (18 - 2m) \]

Thus, we conclude that the correct choice given the associative property is:

(30m + 21m) + (18 - 2m).